Do you have a similar metaphor for _reading_ mathematics? It often seems like reading through a solution gives me a long string of easy to follow navigational directions, but after I get there I have no bird's eye view of the space I moved through.
(cue: "you never 'just read' mathematics!")
I know you're probably going to say something like:
... but I find it hard to believe that this is how you always do it (that'd take an awful lot of time!)